I wanted to know if someone would be able to help me out. I have these 2 questions that I wanted to solve. It's been quite a few years since I have done any type of circuitry I wanted to see if someone can help refresh my memory. If you can explain how you got the answer it would be greatly appreciated. Thanks again

Do we really need the tip? I just don't know how to use this tip to solve the problem.
If Ib can be determined then Ic =βIb.

Click to expand...

Okay. What's β equal to?

It's a poorly designed circuit because it's behavior is completely dependent on the actual value of β.

It's fine to assume that β=100 (or whatever other reasonable value you choose) when working with many (most?) small signal transistors -- provided that the circuit is not particularly sensitive to the actual value of β ! A good circuit should (and it's not always possible) behave acceptably with a value of β that is a factor of 3 or 4 lower or a factor of 3 or 4 higher (a range of about an order of magnitude, but at least a couple of octaves) compared to the value you pick for design purposes.

I don't know exactly but I think each transistor comes with its own range of β. And maybe it is constant at a given temperature. Then depends on the ambient
temperature to choose a proper value from some given table showing the relation between β and T.
This is only what I imagine, not sure right or not.

I don't know exactly but I think each transistor comes with its own range of β. And maybe it is constant at a given temperature. Then depends on the ambient
temperature to choose a proper value from some given table showing the relation between β and T.
This is only what I imagine, not sure right or not.

Click to expand...

Well, let's explore that.

But first let's take a step back and look at this particular circuit. The first thing to note is that, for this particular circuit, the collector current needs to be less than about 1/10 of the base current to keep the transistor from saturating. So if the β is more than about 0.1, the collector voltage will be Vcesat. This is, to say the least, a pretty safe assumption to make (it's probably true even if you put the transistor in backwards!). So the collector voltage will be about 0.2V, give or take a bit. This was most likely the intent of the person writing the problem - to see if you recognize that the transistor is big-time saturated.

So let's shift gears and look at the general case in which the resistor values aren't spec'ed or, to have numbers to work with, let's choose Rb=100kΩ and Rc=1kΩ.

The voltage across the base resistor is Vcc-Vbe, so the base current is

Ib = (Vcc-Vbe)/Rb

The collector current is Ic = βIb and the collector voltage (aka, point B) is

Vc = Vcc-IcRc

So

Vc = Vcc - βIbRc
Vc = Vcc - β[(Vcc-Vbe)(Rc/Rb)]

If we take Vbe≈0.7V, then we have

Vc = 5V - β[(5V - 0.7V)(1kΩ/100kΩ)
Vc = 5V - β*0.043V

Assuming we are talking about a small-signal Si NPN BJT, let's pick a really common one, the 2n3904.

The max β, at 25°C, is spec'ed as 300. But the minimum varies from 40 at a collector current of 0.1mA to 100 at a collector current of 10mA and back down to 30 at a collector current of 100mA. And these specs are not only limited to 25°C, but also to when the collector-emitter voltage is 1.0V.

But let's go with just this for now. What is β? Well, it's somewhere between 30 and 300. Remember that order of magnitude I was talking about?

So at the low end, β=30 and Vc=3.71V. But if β=100, then Vc=0.7V. Note that this is just the range in the MINIMUM value of β at a single temperature. The transistor saturates for β more than about 110.

So let's choose Rc such that Vc is close to, but not at, Vcesat for the maximum value of β. For Vc=0.5V when β=300, we need a collector resistor of 350Ω. But if β turns out to be 30, then Vc will be ≈4.55V.

Do you see how the results are all over the map?

And that's before we start looking at how β varies if we don't require T=25°C or Vce=1.0V. To get a feeling for that, look at the very first plot in the Typical Performance Characteristics (and note that these are "typical" values, not min/max). You can see that the typical β varies from less than 150 at low temp up to nearly 400 at high temp (and these are all at Vce=5.0V). So there is another factor of three to throw into the mix.

The bottom line is that the relation Ic=βIb is nice and tidy on paper (and it has its uses in the real world, don't get me wrong), but everytime you use it you need to say to yourself, "Will me results be worthless if the value I use for β is wrong by an order of magnitude?" If the answer is yes, then you have a poor design (or are doing the analysis in a poor way).